Determination of the frequencies and forms of free vibrations of pentagonal plates by the finite-element method

  • A. Ya. Grigorenko Institute of Mechanics after S.P. Tymoshenko NAS of Ukraine, 83000, Kyiv, Nesterov st., 3
  • M. Yu. Borysenko Institute of Mechanics after S.P. Tymoshenko NAS of Ukraine, 83000, Kyiv, Nesterov st., 3
  • O. V. Boychuk Nikolaev National Agrarian University, 54030, Nikolaev, Georgy Gongadze st., 9 https://orcid.org/0000-0003-1592-3660

Abstract

Frequencies and modes of free vibrations of an isotropic thin pentagonal plate of regular shape with various configurations of rigid attachment at the edges are determined using the finite element method (FEM). The results obtained for some pentagonal plates are compared with the results obtained for square plates of an equivalent mass with corresponding boundary conditions. We present the vibration modes of the studied plates and the topology of the vibration modes for some of the considered plates corresponding to the square plates with free edges and rigidly fixed edges. The reliability of the obtained results is ensured by the use of a substantiated mathematical model, the correct formulation of the problem and the practical convergence of the calculated frequencies when using the FEM.

Key words: finite element method, pentagonal plate, frequency and shape of free vibrations.

Pages of the article in the issue: 61 - 66

Language of the article: Ukrainian

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How to Cite
Grigorenko, A. Y., Borysenko, M. Y., & Boychuk, O. V. (1). Determination of the frequencies and forms of free vibrations of pentagonal plates by the finite-element method. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, (1-2), 61-66. https://doi.org/10.17721/1812-5409.2020/1-2.10
Section
Differential equations, mathematical physics and mechanics